| Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer. |
A) If\[x>y\]
B) If \[x\ge y\]
C) If\[x<y\]
D) \[x\le y\]
E) If \[x=y\]or the relationship cannot be established
Correct Answer: B
Solution :
| [b] I. \[{{x}^{2}}-10x+24=0\] |
| \[\Rightarrow \]\[{{x}^{2}}-6x-4x+24=0\] |
| \[\Rightarrow \]\[x\,(x-6)-4\,(x-6)=0\] |
| \[\Rightarrow \]\[(x-4)(x-6)=0\] |
| \[\Rightarrow \] \[x=4,\]6 |
| II. \[{{y}^{2}}-9y+20=0\] \[\Rightarrow \]\[{{y}^{2}}-5y-4y+20=0\] |
| \[\Rightarrow \]\[y\,(y-5)-4\,(y-5)=0\] |
| \[\Rightarrow \]\[(y-4)\,\,(y-5)=0\] |
| \[\Rightarrow \] \[y=4,\]\[y=5\] |
| \[\therefore \]\[x\ge y\] |
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